Find the Distance Between Two Points (0,1) and (6,3.5)

$(0, 1)$ and $(6, 3.5)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

$\sqrt{{(6 - 0)}^{2} + {(3.5 - 1)}^{2}}$

Simplify.

Subtract $0$ from $6$ .

$\sqrt{6^{2} + {(3.5 - 1)}^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{36 + {(3.5 - 1)}^{2}}$

Subtract $1$ from $3.5$ .

$\sqrt{36 + {2.5}^{2}}$

Raise $2.5$ to the power of $2$ .

$\sqrt{36 + 6.25}$

Add $36$ and $6.25$ .

$\sqrt{42.25}$

Rewrite $42.25$ as ${6.5}^{2}$ .

$\sqrt{{6.5}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$6.5$